arXiv subjects

Imre Varga

Publications and source records attributed to Imre Varga.

30 records · Page 2Linked to original sources

arXiv2000

Correlations and fluctuations of matrix elements and cross sections

The fluctuations and correlations of matrix elements of cross sections are investigated in open systems that are chaotic in the classical limit. The form of the correlation functions is discussed within a statistical analysis and tested in calculations for a damped quantum kicked rotator. We briefly comment on the modifications expected for systems with slowly decaying correlations, a typical feature in mixed phase spaces.

nlin.CD↗

arXiv2000

Semiclassical cross section correlations

We calculate within a semiclassical approximation the autocorrelation function of cross sections. The starting point is the semiclassical expression for the diagonal matrix elements of an operator. For general operators with a smooth classical limit the autocorrelation function of such matrix elements has two contributions with relative weights determined by classical dynamics. We show how the random matrix result can be obtained if the operator approaches a projector onto a single initial state. The expressions are verified in calculations for the kicked rotor.

nlin.CD↗

arXiv2000

Classical fluctuations and semiclassical matrix elements

We discuss the fluctuation properties of diagonal matrix elements in the semiclassical limit in chaotic systems. For extended observables, covering a phase space area of many times Planck's constant, both classical and quantal distributions are Gaussian. If the observable is a projection onto a single state or an incoherent projection onto several states classical and quantal distribution differ, but the mean and the variance are still obtainable from classical considerations.

nlin.CD↗

arXiv2000

Critical statistics in a power-law random banded matrix ensemble

We investigate the statistical properties of the eigenvalues and eigenvectors in a random matrix ensemble with $H_{ij}\sim |i-j|^{-μ}$. It is known that this model shows a localization-delocalization transition (LDT) as a function of the parameter $μ$. The model is critical at $μ=1$ and the eigenstates are multifractals. Based on numerical simulations we demonstrate that the spectral statistics at criticality differs from semi-Poisson statistics which is expected to be a general feature of systems exhibiting a LDT or `weak chaos'.

cond-mat.dis-nn↗

arXiv1999

One-parameter Superscaling at the Metal-Insulator Transition in Three Dimensions

Based on the spectral statistics obtained in numerical simulations on three dimensional disordered systems within the tight--binding approximation, a new superuniversal scaling relation is presented that allows us to collapse data for the orthogonal, unitary and symplectic symmetry ($β=1,2,4$) onto a single scaling curve. This relation provides a strong evidence for one-parameter scaling existing in these systems which exhibit a second order phase transition. As a result a possible one-parameter family of spacing distribution functions, $P_g(s)$, is given for each symmetry class $β$, where $g$ is the dimensionless conductance.

cond-mat.dis-nn↗

arXiv1998

Comment on ``Critical Behavior in Disordered Quantum Systems Modified by Broken Time--Reversal Symmetry''

In a recent Letter [Phys. Rev. Lett. 80, 1003 (1998)] Hussein and Pato employed the maximum entropy principle (MEP) in order to derive interpolating ensembles between any pair of universality classes in random matrix theory. They apply their formalism also to the transition from random matrix to Poisson statistics of spectra that is observed for the case of the Anderson-type metal-insulator transition. We point out the problems with the latter procedure.

cond-mat.dis-nn↗

arXiv1998

Spectral Properties of the Chalker-Coddington Network

We numerically investigate the spectral statistics of pseudo-energies for the unitary network operator U of the Chalker--Coddington network. The shape of the level spacing distribution as well the scaling of its moments is compared to known results for quantum Hall systems. We also discuss the influence of multifractality on the tail of the spacing distribution.

cond-mat.mes-hall↗

arXiv1997

The generalized localization lengths in one dimensional systems with correlated disorder

The scale invariant properties of wave functions in finite samples of one dimensional random systems with correlated disorder are analyzed. The random dimer model and its generalizations are considered and the wave functions are compared. Generalized entropic localization lengths are introduced in order to characterize the states and compared with their behavior for exponential localization. An acceptable agreement is obtained, however, the exponential form seems to be an oversimplification in the presence of correlated disorder. According to our analysis in the case of the random dimer model and the two new models the presence of power-law localization cannot be ruled out.

cond-mat.dis-nn↗

arXiv1997

Novel Scaling Relation of the Energy Spacing Distribution in Quantum-Hall Systems

The shape analysis of the energy spacing distribution $P(s)$ obtained from numerical simulation of two dimensional disordered electron systems subject to strong magnetic fields is performed. In the present work we reanalyze the data obtained in a previous publication. Special moments of the $P(s)$ function related to Rényi-entropy differences show a novel scale invariant relation that is attributed to the presence of one-parameter scaling. This relation seems to show both deviations and universality depending on which Landau-band is considered and whether the disorder is correlated or uncorrelated. Furthermore, our analysis shows the existence of an huge, however, irrelevant length scale in the case of the second lowest Landau-band and no disorder correlations that completely disappears with the introduction of disorder correlations on the range of one magnetic length.

cond-mat.mes-hall↗

arXiv1996

Multifractality beyond the Parabolic Approximation: Deviations from the Log-normal Distribution at Criticality in Quantum Hall Systems

Based on differences of generalized Rényi entropies nontrivial constraints on the shape of the distribution function of broadly distributed observables are derived introducing a new parameter in order to quantify the deviation from lognormality. As a test example the properties of the two--measure random Cantor set are calculated exactly and finally using the results of numerical simulations the distribution of the eigenvector components calculated in the critical region of the lowest Landau--band is analyzed.

cond-mat.mes-hall↗

arXiv1994

Shape Analysis of the Level Spacing Distribution around the Metal Insulator Transition in the Three Dimensional Anderson Model

We present a new method for the numerical treatment of second order phase transitions using the level spacing distribution function $P(s)$. We show that the quantities introduced originally for the shape analysis of eigenvectors can be properly applied for the description of the eigenvalues as well. The position of the metal--insulator transition (MIT) of the three dimensional Anderson model and the critical exponent are evaluated. The shape analysis of $P(s)$ obtained numerically shows that near the MIT $P(s)$ is clearly different from both the Brody distribution and from Izrailev's formula, and the best description is of the form $P(s)=c_1\,s\exp(-c_2\,s^{1+β})$, with $β\approx 0.2$. This is in good agreement with recent analytical results.

cond-mat↗

arXiv1994

Information Length and Localization in One Dimension

The scaling properties of the wave functions in finite samples of the one dimensional Anderson model are analyzed. The states have been characterized using a new form of the information or entropic length, and compared with analytical results obtained by assuming an exponential envelope function. A perfect agreement is obtained already for systems of $10^3$--$10^4$ sites over a very wide range of disorder parameter $10^{-4}<W<10^4$. Implications for higher dimensions are also presented.

cond-mat↗